Package 'NetPreProc' reference manual

Title:	Network Pre-Processing and Normalization
Description:	Network Pre-Processing and normalization. Methods for normalizing graphs, including Chua normalization, Laplacian normalization, Binary magnification, min-max normalization and others. Methods to sparsify adjacency matrices. Methods for graph pre-processing and for filtering edges of the graph.
Authors:	Giorgio Valentini [aut, cre]
Maintainer:	Giorgio Valentini <[email protected]>
License:	GPL (>= 2)
Version:	1.2
Built:	2025-01-23 04:55:06 UTC
Source:	https://github.com/cran/NetPreProc

NetPreProc

Description

Network Pre-Processing and normalization.

Details

Package:	NetPreProc
Type:	Package
Version:	1.2
Date:	2022-09-14
License:	GPL (>= 2)
LazyLoad:	yes
Depends:	methods
Imports:	graph
Suggests:	bionedata

Network Pre-Processing and normalization. Methods for normalizing graphs, including Chua normalization, Laplacian normalization, Binary magnification, min-max normalization and oters. Methods to sparsify adjacency matrices. Methods for graph pre-processing and for filtering edges of the graph.

Author(s)

Giorgio Valentini – Universita' degli Studi di Milano

Maintainer: Giorgio Valentini<[email protected]>

Transforming a real-valued network matrix into a binary matrix

Description

Methods to transform a a real-valued network matrix into a binary matrix. The binary matrix is obtained by thresholding: values above the given threshold are set to 1, otherwise to 0

Usage

Binary.matrix.by.thresh(W, thresh=0.5)
Binary.matrix.by.thresh(W, thresh=0.5)

Arguments

`W`	an object representing the graph to be normalized
`thresh`	the threshold (def.=0.5)

Value

The normalized binary adjacency matrix of the network

Methods

signature(W = "graph"): an object of the virtual class graph (hence including objects of class graphAM and graphNEL from the package graph)
signature(W = "matrix"): a matrix representing the adjacency matrix of the graph

Examples

library(bionetdata);
data(DD.chem.data);
W <- Binary.matrix.by.thresh(DD.chem.data);

# Using both methods with both signatures "matrix" and "graph"
# reducing dimension of the graph
library(graph);
DD.chem.data.red <- DD.chem.data[1:100,1:100];
W.red <- Binary.matrix.by.thresh(DD.chem.data.red);
g <- new("graphAM", adjMat=DD.chem.data.red, values=list(weight=DD.chem.data.red));
Wg <- Binary.matrix.by.thresh(g);
any(W.red!=Wg);
library(bionetdata);
data(DD.chem.data);
W <- Binary.matrix.by.thresh(DD.chem.data);

# Using both methods with both signatures "matrix" and "graph"
# reducing dimension of the graph
library(graph);
DD.chem.data.red <- DD.chem.data[1:100,1:100];
W.red <- Binary.matrix.by.thresh(DD.chem.data.red);
g <- new("graphAM", adjMat=DD.chem.data.red, values=list(weight=DD.chem.data.red));
Wg <- Binary.matrix.by.thresh(g);
any(W.red!=Wg);

Graph checking

Description

Method to check the characteristics of a graph. Check if its adjacency matrix is symmetric, if it has NA, NaN o Inf values, and some minimals statistics about nodes and edges.

Usage

check.network(W, name="Network matrix")
check.network(W, name="Network matrix")

Arguments

`W`	an object representing the graph to be checked
`name`	a character vector that will be printed as heading

Value

It return a list of strings about the characteristics of the graph

Methods

signature(W = "graph"): an object of the virtual class graph (hence including objects of class graphAM and graphNEL from the package graph)
signature(W = "matrix"): a matrix representing the adjacency matrix of the graph

Examples

library(bionetdata);
data(DD.chem.data);
check.network(DD.chem.data);
W <- Prob.norm(DD.chem.data);
check.network(W, "prob. transition matrix");
WL <- Laplacian.norm(DD.chem.data);
check.network(WL, "Laplacian norm. matrix");

library(graph)
g1 = randomEGraph(LETTERS[1:15], edges = 40);
check.network(g1, "random graph");
library(bionetdata);
data(DD.chem.data);
check.network(DD.chem.data);
W <- Prob.norm(DD.chem.data);
check.network(W, "prob. transition matrix");
WL <- Laplacian.norm(DD.chem.data);
check.network(WL, "Laplacian norm. matrix");

library(graph)
g1 = randomEGraph(LETTERS[1:15], edges = 40);
check.network(g1, "random graph");

Chua normalization

Description

Normalization of graphs according to Chua et al., 2007. The normalized weigths between nodes are computed by taking into account their neighborhoods. This normalization is meaningful in particular with interaction data. More precisely, the normalized weigth $W_{ij}$ between nodes $i$ and $j$ is computed by taking into account their neighborhods $N_i$ and $N_j$ :

$W_{ij} = \frac{2|N_i \cap N_j|}{|N_i \setminus N_j| + 2|N_i \cap N_j| + 1}\times \frac{2|N_i \cap N_j|}{|N_j \setminus N_i| + 2|N_i \cap N_j| + 1}$

where $N_k$ is the set of the neighbors of gene $k$ ( $k$ is included).

Usage

Chua.norm(W)
Chua.norm(W)

Arguments

`W`	an object representing the graph to be normalized

Value

The normalized adjacency matrix of the network

Methods

signature(W = "graph"): an object of the virtual class graph (hence including objects of class graphAM and graphNEL from the package graph)
signature(W = "matrix"): a matrix representing the adjacency matrix of the graph

References

Chua, H., Sung, W., & Wong, L. An efficient strategy for extensive integration of diverse biological data for protein function prediction. Bioinformatics, 23 , 3364–3373, 2007.

Examples

library(bionetdata);
data(Yeast.Biogrid.data);
W <- Chua.norm(Yeast.Biogrid.data);
library(bionetdata);
data(Yeast.Biogrid.data);
W <- Chua.norm(Yeast.Biogrid.data);

Construction of the Pearson correlation matrix

Description

Function to obtain the Pearson correlation matrix between rows of a given matrix.

Usage

Do.sim.matrix.Pearson(M, cut = TRUE, remove.negatives = TRUE, min.thresh = 0)
Do.sim.matrix.Pearson(M, cut = TRUE, remove.negatives = TRUE, min.thresh = 0)

Arguments

`M`	input matrix
`cut`	if TRUE (def.) at least one edge is maintained for each node, all the other edges are set to 0. If false no edgeis set to 0.
`remove.negatives`	if TRUE (def) negative values are replaced with 0 in the correlation matrix
`min.thresh`	minimum allowed threshold (def. 0). If a threshold lower than min.thresh is selected, thanit is substituted by min.thresh. Warning: setting min.thresh to large values may lead to highly disconneted network

Details

You can also "sparsify" the matrix, by putting to 0 all the weights, by setting a threshold such that at least one edge is maintained for each node. The diagonal values are set to 0.

Value

a square symmetric matrix of the Pearson correlation coefficients computed between the rows of M

Examples

# a gaussian random matrix
D <- matrix(rnorm(20000),nrow=200);
W <- Do.sim.matrix.Pearson (D);
# the same without default parameters
W2 <- Do.sim.matrix.Pearson (D, cut=FALSE, remove.negatives=FALSE, min.thresh=-20);
# a gaussian random matrix
D <- matrix(rnorm(20000),nrow=200);
W <- Do.sim.matrix.Pearson (D);
# the same without default parameters
W2 <- Do.sim.matrix.Pearson (D, cut=FALSE, remove.negatives=FALSE, min.thresh=-20);

Laplacian graph normalization

Description

Methods to normalize weights of square symmetric adjacency matrices. A network matrix is normalized by dividing each entry $W_{ij}$ by the square root of the product of the sum of elements of row $i$ and the sum of the elemnts in column $j$ . In other words if $D$ is a diagonal matrix such that $D_{ii} = \sum_j W_{ij}$ , then the normalize matrix is:

$W_{norm} = D^{-1/2} W D^{-1/2}$

Usage

Laplacian.norm(W)
Laplacian.norm(W)

Arguments

`W`	an object representing the graph to be normalized

Value

The normalized adjacency matrix of the network

Methods

signature(W = "graph"): an object of the virtual class graph (hence including objects of class graphAM and graphNEL from the package graph)
signature(W = "matrix"): a matrix representing the adjacency matrix of the graph

Examples

library(bionetdata);
# normalization of drug-drug similarity networks
data(DD.chem.data);
W <- Laplacian.norm(DD.chem.data);
# the same using an object of class graphAM
g <- new("graphAM", adjMat=DD.chem.data, values=list(weight=DD.chem.data));
Wg <- Laplacian.norm(g);
library(bionetdata);
# normalization of drug-drug similarity networks
data(DD.chem.data);
W <- Laplacian.norm(DD.chem.data);
# the same using an object of class graphAM
g <- new("graphAM", adjMat=DD.chem.data, values=list(weight=DD.chem.data));
Wg <- Laplacian.norm(g);

Normalization of binary matrices

Description

Normalization of binary matrices according to the procedure described in Mostafavi et al. 2008. Having a binary matrix M, for each feature, if b is the proportion of 1, then ones are replaced with -log(b) and zeros with log(1-b).

Usage

Magnify.binary.features.norm(M)
Magnify.binary.features.norm(M)

Arguments

`M`	an object representing the matrix to be normalized

Value

The normalized matrix

Methods

signature(M = "matrix"): Input binary matrix. Rows are examples, columns features

References

Mostafavi, S., Ray, D., Warde-Farley, D., Grouios, C., & Morris, Q. GeneMANIA: a real-time multiple association network integration algorithm for predicting gene function. Genome Biology, 9, 2008.

Examples

D <- matrix(ifelse(runif(40000)>0.9,1,0),nrow=100);
M <- Magnify.binary.features.norm(D);
D <- matrix(ifelse(runif(40000)>0.9,1,0),nrow=100);
M <- Magnify.binary.features.norm(D);

Max-min graph normalization

Description

Graph normalization with respect to the minimum and maximum value of its weights. Each entry of the normalized matrix is in the range $[0..1]$ :

$W_{norm} = \frac{(W - \min(W))}{(\max(W)-\min(W))}$

Usage

Max.Min.norm(W)
Max.Min.norm(W)

Arguments

`W`	an object representing the graph to be normalized

Value

The normalized adjacency matrix of the network

Methods

signature(W = "graph"): an object of the virtual class graph (hence including objects of class graphAM and graphNEL from the package graph)
signature(W = "matrix"): a matrix representing the adjacency matrix of the graph

Examples

library(bionetdata);
# max-min normalization for a drug-drug similarity network
data(DD.chem.data);
W <- Max.Min.norm(DD.chem.data);
# the same using an object of class graphAM 

g <- new("graphAM", adjMat=DD.chem.data, values=list(weight=DD.chem.data));
Wg <- Max.Min.norm(g);
library(bionetdata);
# max-min normalization for a drug-drug similarity network
data(DD.chem.data);
W <- Max.Min.norm(DD.chem.data);
# the same using an object of class graphAM 

g <- new("graphAM", adjMat=DD.chem.data, values=list(weight=DD.chem.data));
Wg <- Max.Min.norm(g);

Probabilistic normalization of a graph

Description

Method to compute the transition probability matrix of network. A network matrix is normalized by dividing each entry $W_{ij}$ by the the sum of elements of row $i$ In other words if $D$ is a diagonal matrix such that $D_{ii} = \sum_j W_{ij}$ then the normalize matrix is:

$W_{norm} = D^{-1} W$

Usage

Prob.norm(W)
Prob.norm(W)

Arguments

`W`	an object representing the graph to be normalized

Value

The normalized transition probability matrix of network

Methods

signature(W = "graph"): an object of the virtual class graph (hence including objects of class graphAM and graphNEL from the package graph)
signature(W = "matrix"): a matrix representing the adjacency matrix of the graph

Examples

library(bionetdata);
# making transition prob matrix for a drug-drug similarity network
data(DD.chem.data);
W <- Prob.norm(DD.chem.data);
# the same using an object of class graphAM and of class graphNEL

g <- new("graphAM", adjMat=DD.chem.data, values=list(weight=DD.chem.data));
Wg <- Prob.norm(g);
g2 <- as(g, "graphNEL");
Wg2 <- Prob.norm(g2);
library(bionetdata);
# making transition prob matrix for a drug-drug similarity network
data(DD.chem.data);
W <- Prob.norm(DD.chem.data);
# the same using an object of class graphAM and of class graphNEL

g <- new("graphAM", adjMat=DD.chem.data, values=list(weight=DD.chem.data));
Wg <- Prob.norm(g);
g2 <- as(g, "graphNEL");
Wg2 <- Prob.norm(g2);

Sparsifying the graph

Description

Methods to sparsify a network matrix. By this method a general threshold is et such that you a minimum of k edges is guranteed for each node

Usage

Sparsify.matrix(W, k=1)
Sparsify.matrix(W, k=1)

Arguments

`W`	an object representing the graph to be sparsified
`k`	the number of guaranteed edges for each node (def.=1)

Value

The sparsified adjacency matrix of the network

Methods

signature(W = "graph"): an object of the virtual class graph (hence including objects of class graphAM and graphNEL from the package graph)
signature(W = "matrix"): a matrix representing the adjacency matrix of the graph

Examples

library(bionetdata);
data(FIN.data);
W <- Laplacian.norm(as.matrix(FIN.data));
# sparsification by maintaining at least one neighbour per node 
W1 <- Sparsify.matrix(W);
# sparsification by maintaining at least 20 neighbours per node (if any)
W20 <- Sparsify.matrix(W, k=20);

library(bionetdata);
data(FIN.data);
W <- Laplacian.norm(as.matrix(FIN.data));
# sparsification by maintaining at least one neighbour per node 
W1 <- Sparsify.matrix(W);
# sparsification by maintaining at least 20 neighbours per node (if any)
W20 <- Sparsify.matrix(W, k=20);

Sparsifying the graph by a fixed number of edges per node

Description

Methods to sparsify a network matrix by fixing the number of edges for each node. It selects the first k neighbours for each node (by row) according to the weight of the edge By this function you select exactly k edges for each node (if there are at least k edges in the adjacency matrix). The resulting matrix is not symmetric.

Usage

Sparsify.matrix.fixed.neighbours(W, k=10)
Sparsify.matrix.fixed.neighbours(W, k=10)

Arguments

`W`	an object representing the graph to be normalized
`k`	the number of edges for each node (def.=10)

Value

a sparsified matrix (Warning: the matrix is not symmetric)

Methods

signature(W = "graph"): an object of the virtual class graph (hence including objects of class graphAM and graphNEL from the package graph)
signature(W = "matrix"): a matrix representing the adjacency matrix of the graph

Examples

library(bionetdata);
data(FIN.data);
W <- Laplacian.norm(as.matrix(FIN.data));
# sparsification with 10 neighbours per node 
W10 <- Sparsify.matrix.fixed.neighbours(W);
# sparsification with 20 neighbours per node 
W20 <- Sparsify.matrix.fixed.neighbours(W, k=20);
library(bionetdata);
data(FIN.data);
W <- Laplacian.norm(as.matrix(FIN.data));
# sparsification with 10 neighbours per node 
W10 <- Sparsify.matrix.fixed.neighbours(W);
# sparsification with 20 neighbours per node 
W20 <- Sparsify.matrix.fixed.neighbours(W, k=20);

Package 'NetPreProc'

Help Index

NetPreProc

Description

Details

Author(s)

Transforming a real-valued network matrix into a binary matrix

Description

Usage

Arguments

Value

Methods

Examples

Graph checking

Description

Usage

Arguments

Value

Methods

Examples

Chua normalization

Description

Usage

Arguments

Value

Methods

References

Examples

Construction of the Pearson correlation matrix

Description

Usage

Arguments

Details

Value

Examples

Laplacian graph normalization

Description

Usage

Arguments

Value

Methods

Examples

Normalization of binary matrices

Description

Usage

Arguments

Value

Methods

References

Examples

Max-min graph normalization

Description

Usage

Arguments

Value

Methods

Examples

Probabilistic normalization of a graph

Description

Usage

Arguments

Value

Methods

Examples

Sparsifying the graph

Description

Usage

Arguments

Value

Methods

Examples

Sparsifying the graph by a fixed number of edges per node

Description

Usage

Arguments

Value

Methods

Examples